Extensible locking systems for formwork for the casting of concrete constructions

ABSTRACT

The present invention relates to apparatus for casting concrete structures having a varying cross-section and includes a plurality of interconnected units. Each of the units includes at least two rods of equal length which are pivotally interconnected to one another at their mid points, the ends of adjacent units being pivotally connected at an angle to one another such that upon pivoting of the two rods of each of the units, the ends are all moved in parallel relationship to one another. A rigid yoke carries the framework and includes a pair of legs, each of the units being pivotally connected to a stationary point on one yoke leg and pivotally connected to a member movable along a yoke leg.

United States Patent 1151 3,659,982 Svensson et al. 1 May 2, 1972 [54] EXTENSIBLE LOCKING SYSTEMS FOR 2,806,747 9/1957 Jaeger ..182/179 FORMWORK FOR THE CASTING 0F 3,045,313 7/1962 Dorn ..25/ 124 X CONCRETE CONSTRUCTIONS 3,187,838 6/1965 Stewart 182/188 X 3,231,043 l/1966 Brown 182/152 X [72] Inventors: Sven-Erik Vllhelm Svensson, Norrbyvagen 3,252,199 /1966 Bossner 249/17 141 43 Huddinse, Sweden; Erno Jozef 3,354,596 11/1967 Schafer ..182/152 x Thoma, Koszta Budapest 972,781 10/1910 Bohland et al. 25/131 s13 gar)! 1,435,488 11/1922 McGregor ..25/124 [22] Filed: June 3, 968 3,053,351 9/1962 Fulcher ..52/109 [21] Appl. No.: 734,079 FOREIGN PATENTS OR APPLICATIONS 792,183 3/1958 Great Britain ..25/131 K [30] Foreign Application Priority Data 1,434,526 12/1968 Germany ..52/ 109 June 2, 1967 Sweden ..7785/67 Primary Examiner Roben D. Baldwin Assistant Examiner-Ben D. Tobor 52 US. Cl ..425/63, 249/ Ammey wimam D. Hall Elliott L Pollock Fred c Phflpm 151 Int. Cl ..E04 11/22 Gem 6 Vande Sande Charles F Steinin er and Robert R 58 FieldofSearch ..25/1B,118l-l,118P, 118R, P 1 g /130A,13lM,13lA-l3l.5A,131.5 5,131.5 Y G, 13] D, 131 EM, 131 RY, 131 J, 131 K, [31 LY,

131SA,131BB,131YP,131YF,131LM,DlG. [57] ABSTRACT 16, 131 131 131 131 YT; 249/17 181 The present invention relates to apparatus for casting 221 1591 1912091212; concrete structures having a varying cross-section and in- 182/152, 1881 187; 52/109 cludes a plurality of interconnected units. Each of the units includes at least two rods of equal length which are pivotally in- [56] References cued terconnected to one another at their mid points, the ends of UNITED STATES PATENTS adjacent units being pivotally connected at an angle to one another such that upon plvotmg of the two rods of each of the 2.431 3/1968 L WC units, the ends are all moved in parallel relationship to one 3,453,707 7/l969 JOhflHSSOW- another. A rigid yoke carries the framework and includes a 97 ,2 2 1 H1910 Higgins pair of legs, each of the units being pivotally connected to a 1,172,355 2/1916 Guest stationary point on one yoke leg and pivotally connected to a MCDOwe u... member movable along a y ke leg 2,516,318 7/1950 Hawes 2,596,854 5/1952 Jack ..25/131 4Claims,36 Drawing Figures Patented May 2, 1972 3,659,982

15 Sheets-Sheet 1 Fig.1

Patented May 2, 1972 3,659,982

15 Sheets-Sheet 5 Patented May 2, 1972 3,659,982

15 Sheets-Sheet 4.

Patented May 2, 1972 15 Sheets-Sheet 5 Patented May 2, 1972 15 Sheets-Sheet 6 Fig.18

Patented May 2,1972 3,659,982

l5 Sheets-Sheet 7 Patented May 2, 1972 3,659,982

15 Sheets-Sheet 8 9 g B an s 3 Fig. 22

15 Sheets-Sheet 9 Patented May 2, 1972 15 Sheets-Sheet lO Patented May 2, 1972 15 Sheets-Sheet ll Fig.26

Patented May 2, 1972 15 Sheets-Sheet l5 Patented May 2, 1972 3,659,982

15 Sheets-Sheet l4 Patented May 2, 1972 15 Sheets-Sheet 15 EXTENSIBLE LOCKING SYSTEMS FOR F ORMWORK FOR THE CASTING OF CONCRETE CONSTRUCTIONS Difficult technical, economic and practical problems are raised by concrete formwork used in the erection of relatively high constructions, such as chimney stacks, television towers, observation towers, pillars of bridges, cooling towers and the like, in which the horizontal cross-section of the construction varies in the direction of its height. ln climbing formwork the concreting is carried out in stages inside a stationary shuttering of predetermined height. When the concrete has set, the formwork for the next casting stage is raised by a distance corresponding to the height of the formwork. In sliding formwork the concreting is performed continuously inside formwork which can move or slide upwards. No matter which of these methods is used, after it has moved upwards, the cross-sectional surface of the formwork must still be changed in one way or another. A progressive upward tapering of the horizontal cross-sectional surface of the concrete construction means that the formwork surface must be reduced or extended. This reduction or extension is a direct function of the geometrical design of the construction.

However, not only the formwork surfacei.e., the shutteringmust be variable or flexible, but the locking system, in which the formwork walls are secured, which represents an integral part of the formwork system, and which takes the pressure of the concrete, must be made variable (flexible), so that the concrete construction will have the required accurate shape at each place over its height. It is just as necessary to be able correspondingly to vary the working bridges attached to the formwork or its locking system for performing the concreting. Moreover, for practical and economic reasons the whole formwork construction-Le, the formwork walls, the locking system and the working bridges-must be regarded as one unit, mounted at the base of the building, and thereafter used undivided for continuous concreting to the top of the building, without repeated dismantling and assembly. Only those adjustments and readjustments of the formwork are inevitable which are the result of the horizontal cross-section gradually changing in the upward direction.

With both climbing and sliding formwork, a number of fairly similar methods are known for constructing the actual formwork walls. With circular cross-sections, or other closed, steadily curved cross-sections, these methods are generally based on so-called overlapping formworki.e., a part of the form work so engages via a thin sheet of metal (the overlapping part) with an adjacent part of the formwork, that with decreasing cross-section of the concrete construction, the overlapping distance in each formwork connection of this kind gradually increases, and decreases. With square, rectangular or polygonal cross-sections, on a change in the cross-section the formwork parts can slide past one another at an angle at the corners of the cross-section.

It has been easier to deal with problems raised by the construction of the formwork walls. Since the formwork walls are relatively thin -about 3 mm with sheet metal formwork and about 30 mm with timber formwork-the walls have readily been given that deformation which corresponds at every instant to the required curvature of the concrete surface with, for instance, a circular cross-section. As regards the prior art principles of construction of the formwork walls, it can certainly be stated that as a whole they cover the possible fields of application and satisfy those practical and economic requirements which are normally made.

In contrast, the difficulty of achieving a practical method of adjustability or flexibility was much greater as regards the locking system receiving the pressure of the concrete behind the formwork walls, and therefore also as regards the pres sure-receiving locking or yoke construction between the two side walls of the formwork. It was necessary to take into account not only this basically horizontal loading by the pressure of the concrete, but also the vertical loading by the formwork, the loading of the locking system itself, the working bridges, and in the case of sliding formwork also the loading produced by the friction between the formwork and the concrete. The whole formwork-supporting and shaping locking construction is subjected to both horizontal and vertical forces, and must therefore be constructed in some way or other in the form of a three-dimensional lattice construction (spatial lattice). The lattice must have enough rigidity to allow at any moment deformations which are not greater than those permissible having regard to the required shape of the concrete construction, while at the same time the lattice must also in practice be readily adjusted. This demand applies in general to both climbing and sliding formwork. However, there is a certain difference between these two different types of formwork.

Climbing formwork needs a relatively small number of laborious readjustments-made at spaced periods of time. in contrast, with sliding formwork the readjustments are continuously being repeated, but as a rule they are very small-continuous readjustment. For erecting concrete constructions of the kind specified hereinbefore, therefore, it has been proved necessary to provide a continuously extensible spatial lattice which is at the same time rigid against the deformation and constantly located in all directions.

The need for rational methods with climbing and sliding formwork for concrete constructions of varying cross-section and great height has suddenly increased. One of the causes of this, for instance, is technical development, more particularly in industry, where health requirements mean that waste gases harmful to health must be discharged at very great heights, so that chimney stacks have to be built up to 300 m and more in height. For static and economic reasons, chimney stacks of this kind must be constructed from concrete and have an upwardly tapering cross-section. For economic reasons, only climbing or sliding formwork can be used, and it has been found more and more that the latter are preferred for techni cal, practical and economic reasons. However, the decisive problem was to find a basic principle for a convenient construction of the steep, continuously extensible spatial lattice. All the prior art constructions were limited to a spatial lattice geometrically and statically of the traditional kind, with frame members and diagonal strutting. The variability or extensibility of these spatial lattices was achieved on the one hand by making all the nodal points of the frame members and diagonal struts pivotable, and on the other hand by enabling the frame members and diagonal struts to be shortened or lengthened by means of screwed connections or the like. A spatial lattice constructed in this way will have a very large number of screwing places, (they may be hundreds) which must be operated by screws to adjust the lattice. For instance, with continuous sliding formwork casting, the lattice must be so adjusted that the sliding formwork is continuously given a horizontal component of movement synchronized with the vertical component of movement, to obtain agreement with the required generatn'x in each vertical plane through the concrete construction. Since the axes of all these screwed connections are adjusted in different directions, it is impossible to operate some or all of them centrally and in synchronism without the use of extremely complicated arrangements. In the prior art systems, therefore, they have always and exclusively been manually operated. The disadvantages were obvious: expensive places of articulation and screwed connections, shortening or lengthening of the linkages of the lattice, which were difficult to programme, a complicated scheme of the screwed connections for the operatives to use, a large number of operatives needed for operation, irregular alternation of the lattice, since it was done at separate places, a large amount of accuracy required from operatives and management, and monotonous jobs.

The invention relates to a continuously variable spatial lattice and starts from a basically novel idea, but it is not exclusively limited to the use of the spatial lattice for concreting with sliding formwork in concrete constructions of the kind specified, but can also be used, for instance, for the climbing formwork of similar concrete structures. It is an object of the method according to the invention to obviate the afore-mentioned disadvantages of prior art construction principles and to provide a lattice which can be varied completely continuously with simple labor-saving devices and is completely rigid against deformation.

The invention therefore relates to a stifiening locking system which bears the formwork and can be used in the erection of concrete constructions of any cross-section which concrete constructions may take, the cross-section varying to any extent heightwise of the construction.

The invention will now be described in greater detail with reference to the accompanying drawings:

FIG. 1 shows by way of example a number of different cross-sections, namely circular, polygonal, square, rectangular and triangular.

FIG. 2 shows examples of vertical generatrices of concrete constructions with different cross-sectional variations the outer configurations of which are indicated by lines I-I, II-II and III-Ill. This Figure relates to constructions with a vertical axis of symmetry, but the axis can also be inclined.

FIG. 3 is a geometric construction illustrating the principle according to the invention.

FIG. 4 shows a schematic geometric construction.

FIG. 5 illustrates a shortening of the scissors type link system shown in FIG. 4.

FIG. 6 shows a construction with added rods and sliding places.

FIG. 7 shows a shortening of the formation shown in FIG. 6.

FIGS. 8-12 show further forms of development of the idea of the invention, at different stages of making a concrete construction.

FIGS. 13 and 14 are plan views of two examples for polygonal locking systems which are constructed on the geometrical principles of the preceding figures.

FIGS. 15-18 show the parallel movement of a line on the geometrical principles according to the invention.

FIGS. 19 and 20 show the application of the idea of the invention to the lateral movement of formwork walls.

FIG. 21 shows the functional relations of the lateral movement of the formwork walls.

FIG. 22 shows a practical example of a locking system according to the invention used with sliding formwork.

FIG. 23 shows a practical example in which the locking system is completely outside the sliding formwork.

FIG. 24 shows the application of the idea of the invention on a variant and simplified principle, according to which steep discs are used instead of rods.

FIG. 25 shows a development of the basic principles of FIG. 24, spatial-element units or modules being built up from discs.

FIGS. 26 and 27 are plan views showing the basic operation of the device shown in FIG. 25.

FIGS. 28 and 29 are diagrammatic vertical sections and perspective views of an upwardly tapering spatial-element system as shown in FIGS. 26 and 27.

FIG. 30 shows diagrammatically the use of a sliding formwork yoke in combination with crossed discs.

FIGS. 31-33 show diagrammatically, to a reduced scale, various operational steps in the use of the yoke shown in FIG. 30.

FIGS. 34 and 35 show the behaviour of the rigid discs when the locking system is narrowed to a predetermined minimum value, and

FIG. 36 shows a practical example of the use in sliding formwork concreting of a locking system built up from flat discs.

In principle, the invention is based on the geometrical arrangement shown in FIG. 3i.e., that two straight rods Al-B2 and A2-B1 of equal length, which intersect one another pivotably at the center 0, always keep their connecting lines Al-Bl and A2-B2 parallel with one another. When a number of identical scissors of the kind are pivotably connected to one another (FIG. 4), therefore, all the lines Al-Bl etc., are parallel with one another. Each change in length of each of the lines Al-Bl etc., causes a corresponding change in the length of the other lines, maintaining the parallelism of the lines (FIG. 5). If one now introduces into a rod system built up in this way the rods Al-Cl etc., and makes the points B1 etc., the sliding places (FIGS. 6 and 7 these rods will therefore always remain parallel with one another. For each particular position of B1 etc., in the condition locked on the rod Al-Cl etc., the linkage represents a framework rod system of determined geometrical shape and composed of scissors units or modules.

If a plan construction composed in this manner is then coupled at the lines AI-Cl etc., with analagous sciss0rs" unite or moduluses with rods Dl-Fl etc. in perpendicular direction to framework Al-Cl etc. and sliding places El etc. (FIGS. 8 and 9), these rods Dl-Fl etc., will also always remain parallel with the rods Al-Cl etc. Since the points B1 etc., are shared in common, the rods will move in parallel in complete synchronism. If the distances A1-A2, A2-A3 etc., are equal to the distances Dl-D2, D2-D3 etc., the result is a geometrically determined rectilinear spatial construction. If, in contrast, the distances are not equal, the result is a curved spatial construction shown diagrammatically in FIG. 10, in which Al-A2 A2-A3 etc., and Dl-D2 =D2-D3 etc., and D1-D2 Al-A2. At any given moment, therefore, a spatial construction basically built up in the manner described can be considered to be composed of identic members A1A2-B2-Bl-E1-E2- D2-D1, which are identical in this case, and the corresponding ones, all the rods Al-Bl etc. and Bl-EI etc. (vertical in this case), having their geometrically determined positions viewed in plan. Each identical vertical change in length of one or more of the rods Al-Bl etc., changes the mutual position in the plan of all these rods in a definite given geometrical relationship.

FIG. 11 shows two geometrically angle-forming scissors" units or moduluses placed at a geometrical angle with common vertical rods or uprights Al-Cl and A2-C2, the units or moduluses each have their own separate sliding place B1 and B2; C1 and C2. The corresponding sliding place of the vertical guide rods or uprights Dl-Fl and D2-F 2 is H1; H2. The parallel movement of the rods Dl-Fl and DZ-FZ in the direction of the rods Al-Cl and A2-C2 can therefore take place without the mutual parallel movement of the last-mentioned rods, as shown in FIG. 12. In the same way, the rods Al-CI and AZ-CZ can be moved mutually in parallel, without the rods Dl-Fl and D2-F2 moving in the direction of the rods AI-C I and A2-C2.

FIGS. 13 and 14 are exemplary plan views of two polygonal looking systems constructed from rods on the geometrical principles disclosed hereinbefore. In both cases, for claritys sake it has been assumed that the external outline AA of the locking system is to be reduced to the size A'A'. Moreover, the Figures show two lateral elevations explaining the geometrical events during the reduction of the looking system. The internal outline D-D remains constant in both cases, this being shown for clarity by the shading along the line D-H. The reference letters used are basically those used hereinbefore. The rods and nodal points correspond to those in FIGS. 11 and 12.

FIGS. 15-18 show diagrammatically how according to the invention the line A-G of the geometrical construction is moved in parallel in the direction of the axis of the construction. The internal radius of the construction has the reference r, and its external radius has the reference H. The horizontal projection of the extensible or flexible disc A-D-H-G has a maximum length a and a minimum length b in the radial direction. In the starting position (FIG. 15) the vertical lines D-H are locally fixed with relation to the horizontal plane by the fact that the two annular closed polygons D-D and H-H have a determined and unalterable outline, as is indicated by the shading along the line D-I-I. The internal radius has the reference r1, so that the length of the external radius R r1 +a. The vertical lines A-G can now be moved in parallel by a distance (a-b), i.e., into the position shown in FIG. 16, in which therefore the external radius R'= r1 b. In these positions the vertical straight lines A-G are now fixed in placci.e., the closed polygons A-A and G-G are locked in a particular configuration (in this case marked by the shading along AG, while the inner polygons DD and l-l-I-l are unlocked. The vertical straight lines D-H can now be moved in parallel by the distance a-b into their innermost positions (FIG. 17). Here the straight lines Dl-I are again locked and the straight lines AG unlocked, and a condition has been reached analagous to that shown in FIG. 15. However, the internal radius has now been reduced to the value r2. The external radius is therefore R r2 a r1 b). Now, in the manner already described, the vertical straight lines A-G can again be moved in parallel by the distance (ab) i.e., into their positions shown in FIG. 18 (R'= r2 b). The process described can then be repeated. In this way, therefore, the plumb lines A-G can be moved as required in parallel in the direction of the central axis of the geometrical construction.

FIGS. 19 and 20 show in principle how, with the aforedescribed geometrical construction A-D-H-C, for instance a moment-rigid yoke l with formwork walls 2 has been disposed on the plumb line A-G, the walls being borne via adjustable supporting elements 3 by the yoke, and being adjustable by means of the supporting elements 3 to any inclination 1-1. This corresponds in principle to the main devices of sliding formwork concreting, the lifting force required to move all the structural components of the construction along the inclined line being provided by means of jacks 4 of known construction.

A locking system built up from the afore-described geometrical arrangement of rods with stationary and sliding places of articulation can be given the required flexibility by forces exclusively parallel with one another, and changes in length of the vertical rods shown in the embodiments illustrated, which extend through the nodal points A and D. The forces for changing the length of the rods can be applied either as compressive forces between A and G; D and H, the vertical rods being moved in parallel towards one another, or as tensile forces, the rods being moved in parallel away from one another. Since all the forces and directions of adjustment are parallel (and in the examples chosen vertical), the arrangements for producing these forces and movements of nodal points can be simplified, standardized and synchronized in a simple manner, and the required movements of the mobile places of articulation can be performed with great accuracy. The system also enables the continuous or successive change in dimension of the locking system to be performed from a single, central operating place. The devices for this central operation can be of various constructions known to an engineer in the art from the prior art.

With a given step-wise movement A 1 (FIG. 21) which is usually constant, in sliding formwork concreting, along any line of inclination l-l (FIGS. 19 and 20), the sliding formwork 2 and the sliding formwork yoke l i.e., the point A, must be moved by a distance A x in the horizontal direction, A 1: depending on the form x fl y) of the generatrix l-I. To produce the horizontal movement A x, in the case illustrated (FIGS. 19 and 20) the radius R must be reduced by a corresponding distance A R. According to the invention, after the geometric events described hereinbefore, this reduction in diameter is produced by lengthening the distance A-G. The movement A z along the line of inclination ll corresponds to the climbing step (lifting step) of the sliding formwork lifting means used, along the climbing rod disposed in the inclination II. With the conventional sliding formwork lifting means, a climbing step of this kind is usually about 25 mm. The required horizontal movement depends on the value of the climbing step, and the form of the line of inclination I-I. The elongation of the distance A-G required in the present case also depends on the length of the rods A-I-I and D-G (which are of equal length), and also on the particular angle between these rods during the lifting of the formwork. The change of the distance A-G required for each lifting step can therefore be predetermined geometrically and mathematically for each stage in height of the sliding formwork over the height of the concrete construction.

The practical example illustrated in FIG. 22 shows a locking system which is built up from rods according to the aforedescribed geometrical construction and is to be used for sliding formwork concreting. In this case the whole locking system is disposed inside the sliding fonnwork. FIG. 22 shows a sliding formwork yoke 1, sliding formwork walls 2, supporting elements 3 between the formwork and the yoke, lifting members (jacks) 4 and climbing rods 4a thereof. In the locking system, the upright 5 connected to the yoke 1 has the reference 50, and the movable part of the upright 5a had the reference 5b. The scissors-like criss-crossing rods, which are basically radially directed and connected to the upright 5a, 5b have the reference 6 and the pivotable places of attachment of the rods 6 to the upright 5a, 5b have the references 6a, 6b. The inwardly and upwardly directed rod 6 is pivotably connected via the place 60 of attachment to an upright 7. The inwardly and downwardly directed rod 6 is attached to the upright 7 via a retaining member 6d sliding along the lower portion of the upright. The scissors-like criss-crossing rods 8 extending basically tangentially are attached at their top ends via places 8a of articulation to the upright 7, and at their bottom ends are slidably and pivotally connected to the bottom part of the upright via a retaining member 8b. The top ends of the upright 7 are interconnected by rods 9 which are all of identical length in the symmetrical construction shown. Conveniently, the rods 9 can be adjusted in length, for instance, are telescopic, and can be locked. The reference 10 designates the device, for instance, a pressurized screw-driving apparatus, for changing the length of the upright 50, 5b. When the cross-section of the concrete construction is reduced, the uprights 5a, 5b must be lengthened.

During sliding formwork casting, the scissors" unit or module 7-9 is locked in a geometrically fixed position at the places 8b. The scissors" unit 5-7, to which the yoke 1 with its formwork 2 is attached, can be so extended by actuating the screw apparatus 10 that the yoke, and therefore the formwork, moves in the radial direction for instance, inwardly that is to say, the horizontal cross-section of the concrete decreases. When the upright 5 has moved in parallel in the direction of the upright 7 by the longest possible distance, the scissors unit 7-9 is adjusted. First of all, the locking of the telescopic rod 9 and of the two sliding retaining members 8b is released. Since the screw apparatus 10 is operated in the opposite direction to the previous direction, the upright 7 is moved in parallel inwards radially opposite the upright 54, 5b by the rod 6 and the shortening of the upright 5a, 5b. This means that the uprights 7 are moved in parallel with one another by the rods 8, the sliding retaining members 8b of the latter being moved in this case downwards. When the upright has been moved as far as possible inwards (during which movement the upright 5a, 5b retains its position unchanged), the sliding retaining members 8b are again locked on the upright 7. Thereafter the sliding casting process can be continued exactly as before.

FIG. 23 shows a practical example of a locking system for sliding formwork casting which is disposed completely outside the sliding formwork. The references, and also the basic operation of the locking system, are completely analagous to those of FIG. 22. When the cross-section of the concrete construction decreases, the uprights 5a, 5b must be shortened.

The foregoing description with reference to FIGS. 3-23 has clarified the idea of the invention, namely to provide a locking system with variable horizontal projection, based on a horizontal parallel movement of vertical rods or uprights which extend through the end points of two intersecting rods pivotably connected to one another at the center. A pair of rods of this kind represents an extensible or flexible disc, and the locking system, as already described, is built up from a number of discs (or modules) of this kind disposed at an angle to one another. In the comers or nodal points two or more units have a common upright.

Maintaining the afore-described principle on which the in vention is based, however, the locking system can be cut down and simplified to achieve the same final result. Instead of the use, as for instance shown in FIG. 13, of two systems of modules in the form of scissors units or discs (the tangential ones A--A and the radial ones A-D, each comprising two rods), two rigid rectangular frames of equal size constructed from rods and being pivotally connected together along a central axis. Maintaining in principle the same reference letters as before, therefore, FIG. 24 shows diagrammatically two discs A3-D3-E4-D4 and A4-D4-H3-B3 of the kind specified, which intersect one another pivotably along the common center line 0. These discs will be referred to hereinafter as primary discs." When these two discs are turned around the axis 00, the surfaces A3-D3-H3-B3 and A4-D4-H4-B4 are moved in parallel in relation to one another, just as the corresponding lines or straight lines already described were moved in parallel with one another. A number of extensible units or modules of this kind can be disposed close beside one another and at an angle in relation to one another with their axes 00 of rotation horizontal (as shown in FIG. 25), and they can be disposed intersecting at a common center 0. Ifthe points A2, A3, etc. and B2, B3 etc. are then connected by lines of equal length, and at the same time the points D2 and D3 etc. and H2 and H3 etc., are made to coincide in pairs, and the resulting surfaces A2-A3-B3-B2 etc., are regarded as steep, the result is a geometrical spatial system having nodal points whose places are determined at every moment. The same thing also applies if the points D2 and D3 etc., and H2 and H3 etc., do not coincide, as long as the surfaces D2-D3- H3-l-I2 etc., and the surfaces A2-A3-D3-D2 etc., are steep.

The geometrical system shown in FIG. 25 is therefore made up of a number of units or moduluses A3-A4-D4-D3-D3- B4-B4-I-I3, all having extensible surfaces parallel in relation to one another, and a number of secondary frames A2-A3- D3-D2-B2-B3-I-l3-H2, (shown in dotted lines in FIG. 24).

If all the primary discs perpendicular to the axes 00 of rotation have a given length and the axes are horizontally orientated (FIG. 25), then for every equal change in length (in this case change in height) of the secondary discs, the horizontal projection of the spatial system thus composed will also change in a given geometrical manner. An increase in the height of the secondary discs produces a reduction of the horizontal projection in the direction of the central axis 0, as shown in FIGS. 26 and 27, in plan view, rotation of the primary frames about their axes of rotation 00 to increase the height of each unit, causes the internal radius r and the external radius R to be shortened, the radial width a of the units remaining constant.

FIGS. 28 and 29 show diagrammatically in vertical section and perspective a basically horizontal round (in practice polygonal) spatial system of the aforementioned moduluses which narrows in the upward direction (only the moduluses extensible in all planes are shown), the vertical section (the secondary disc) being shown in its starting position (FIG. 28) by the reference A-D-I-I-B. A certain distance higher, the spatial system has changed as shown in FIG. 29, the vertical section, (the secondary disc) having assumed the form AD -l-I. As indicated in FIGS. 28 and 29, the system can be employed to adjust the positions of formwork walls 2 carried by a sliding formwork ridged yoke 1 through adjustable supporting members 3 in a similar manner to that described above with reference to FIGS. 19 and 20, to take account of the variations in horizontal cross-section of a tapering concrete structure to be produced with the aid of the formwork.

FIG. 30 shows diagrammatically an example of how in principle a sliding formwork yoke 1 can be combined with the coupled secondary discs A2-D2-I-I2-B2 and A3-D3-H3-B3. The reference denotes a yoke leg disposed in bending-resistant manner on a horizontal top yoke beam 1a and bottom yoke beam lb, and the reference 12 denotes a displaceable yoke leg which can be applied at various places along the yoke beams la, 1b. Attached in bending-resistant manner between the top and bottom yoke beams la, 1b is a vertical upright M, which therefore co-operates with the yoke leg 1c and the yoke beams la, lb to form a rigid disc (modulus). The rod B3-H3 of a first primary frame (shown in full in FIG. 34) is pivotally connected to one end of each lower (as seen in FIG. 30) secondary frame horizontal member, the corresponding rod of a second primary frame being connected to the other ends of said horizontal members. The rod All-D3 of the first primary frame is connected to one end of each of the upper (as seen in FIG. 30) secondary frame horizontal member, the corresponding rod of the second primary frame being connected to the other ends of these horizontal members which extend from a structure 1 f which is slidable along the uprights 1c and Id. The angles defined by said rods 834-13 and A3-D3 and their corresponding rods of the second primary frame can be adjusted by engaging the rods in selected holes in the horizontal members A2-A3 and B2 -B3. The structure If is movable along the uprights 1c and It! in the direction of the arrows P by screw apparatus 10 (mentioned above) to adjust the vertical dimensions of frames in accordance with the inclination of the wall to be concreted, the yoke being shifted rightwardly (as seen in FIG. 30).

FIGS. 31-33 show diagrammatically to a reduced scale the appearance of the afore-described yoke when the adjustable yoke leg 12 has been locked in various positions to obtain various distances between the two sliding formwork walls 2 i.e., different thicknesses of the concrete wall. For the rest, the references are identical with those in FIGS. 19 and 20.

If, for instance, the locking system is narrowed, for purely practical reasons in the starting position the angle A4-0-A3 (FIG. 34) can be given only a particular maximum value, and in the end position only a particular minimum value. This largest possible change of angle means, with a given length of the distance A4-B3 (equal to the distance A3-B4), that the points A3 and A4 (B3 and B4 etc.) can approach one another only by about one-half of their original distance from one another i.e., the periphery of the formwork can be reduced only by about one-half, and so therefore can the diameter of the cement construction. However, with conical concrete chimney stacks, for instance, the initial diameter at the base conventionally decreases to about one-third with increasing height. To allow this considerable tapering of the cross-section. without, for instance, having to disconnect each second formwork yoke (secondary disc element), which would be an expensive and time-wasting process, the primary discs A3-D3- H4-B4 and A4-D4-H3-B3 etc., can be made adjustable in their length perpendicular to the axis 00 of rotation, but while maintaining the bending or moment-rigidity in the disc plane. FIG. 35 therefore shows how the primary discs have been reduced to their new surfaces A3D3I-l4-B4 and A4-D4-H3-B3. In construction the frame rods A3-B3 and Dh-H3, and A3-B4 and D3-H4 can, for instance, be telesc opic and lockable in precisely determined position thus ensuring precisely determined lengths of the rods. In practice, when changing over to a new starting position in this way, the locking is released, whereafter the force P (FIG. 30) is brought into operation in the opposite direction i.e., the secondary discs in FIG. 30 are given a smaller height. Since the fonnwork yokes remain in their positions, the primary discs experience synchronous, uniform shortening. When the required shortening has been reached, the frame rods are locked, and the operation (sliding formwork concreting) can be continued.

FIG. 36 shows a practical example of how a locking system basically built up from flat discs by means of moment-rigid frames, with the afore-described geometrical manner of construction, can be used in practical sliding formwork concreting. The equipment, consisting of locking system, yokes and sliding formwork, is shown applied to a concrete construction, such as a chimney stack of upwardly narrowing circular crosssection. For simplicitys sake, the sliding formwork yoke with its two yoke legs 1c is stationary, and completed by the yoke beams la, 1b to form a moment-rigid yoke. As in FIG. 22, the 

1. A locking system composed of a plurality of interconnected units for the local support and fixing of formwork for the casting of concrete structures having a cross-section varying along a substantially vertical major axis, each of said units comprising at least two rods of equal length which cross each other and are pivotally interconnected to one another at their midpoints by substantially horizontal shafts disposed centrally of the associated unit, the ends of adjacent units being so pivotally connected at an angle to one another that on pivoting said two rods of each of the units said ends are all moved in parallel relationship to one another, whereby the horizontal size of the locking system structure is changed in geometrical relationship to the variation of the angle of pivoting of said rods, and a yoke which is rigid and which bears the formwork being connected with the connected ends of adjacent units, said yoke comprising two interconnected yoke legs, the units being connected partly pivotally to a stationary point directly on onE yoke leg and partly pivotally to a holder movable along the yoke leg.
 2. A locking system composed of a plurality of interconnected units for the local support of formwork for the casting of concrete structures having a cross-section varying along a substantially vertical major axis, each of said units comprising at least two rods of equal length which cross each other and are pivotally interconnected to one another at their midpoints by substantially horizontal shafts disposed centrally of the associated unit, the ends of adjacent units being so pivotally connected at an angle to one another that on pivoting said two rods of each of the units said ends are all moved in parallel relationship to one another, whereby the horizontal size of the locking system structure is changed in geometrical relationship to the variation of the angle of pivoting of said rods, and a moment-rigid yoke bearing the formwork being connected with the connected ends of adjacent units, the yoke comprises two yoke legs and at least one transverse beam interconnecting the yoke legs, the units being partly pivotally connected to a fixed point on at least one of the yoke legs and partly pivotally connected to a transverse beam disposed for movement along the yoke legs.
 3. A locking system composed of a plurality of interconnected units for the local support and fixing of formwork for the casting of concrete structures having a cross-section varying along a substantially vertical major axis, each of said units comprising at least two rods of equal length which cross each other and are pivotally interconnected to one another at their midpoints by substantially horizontal shafts disposed centrally of the associated unit, the ends of adjacent units being so pivotally connected at an angle to one another that on pivoting said two rods of each of the units said ends are all moved in parallel relationship to one another, whereby the horizontal size of the locking system structure is changed in geometrical relationship to the variation of the angle of pivoting of said rods, and a rigid yoke having a yoke leg, a member displaceable along the yoke leg, a movable part of the locking system being pivotally connected to said displaceable member, a fixed part of the locking system being pivotally connected to a fixed part of the yoke.
 4. A locking system as set forth in claim 1, characterized in that disposed on each formwork yoke is screw means having a direction of operation which is common to all yokes, the device being positioned and constructed so that it can be controlled synchronously from a common control point. 